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Leokris [45]
3 years ago
11

Determine the rational zeros for the function f(x)=x^3+7x^2+7x-15

Mathematics
2 answers:
Dimas [21]3 years ago
5 0

Answer:

Actual rational zeros of f(x) are x=-5, x=-3, and x=1.

Step-by-step explanation:

Given function is f(x)=x^3+7x^2+7x-15.

constant term = p = -15

coefficient of leading term q= 1

then possible rational roots of given function f(x) are the divisors of \pm \frac{p}{q}=\pm 1, \quad \pm 3, \quad \pm 5, \quad \pm 15

Now we can plug those possible roots into given function to see which one of them gives output 0.

test for x=1

f(x)=x^3+7x^2+7x-15

f(1)=1^3+7(1)^2+7(1)-15

f(1)=1+7+7-15

f(1)=0

Hence x=1 is the actual rational zero.

Similarly testing other roots, we get final answer as:

Actual rational zeros of f(x) are x=-5, x=-3, and x=1.

alexandr402 [8]3 years ago
4 0

Answer:

1,-3,-5

Step-by-step explanation:

Given:

f(x)=x^3+7x^2+7x-15

Finding all the possible rational zeros of f(x)

p= ±1,±3,±5,±15 (factors of coefficient of last term)

q=±1(factors of coefficient of leading term)

p/q=±1,±3,±5,±15

Now finding the rational zeros using rational root theorem

f(p/q)

f(1)=1+7+7-15

   =0

f(-1)= -1 +7-7-15

     = -16

f(3)=27+7(9)+21-15

    =96

f(-3)= (-3)^3+7(-3)^2+7(-3)-15

     = 0

f(5)=5^3+7(5)^2+7(5)-15

    =320

f(-5)=(-5)^3+7(-5)^2+7(-5)-15

      =0    

f(15)=(15)^3+7(15)^2+7(15)-15

     =5040

f(-15)=(-15)^3+7(-15)^2+7(-15)-15

      =-1920

Hence the rational roots are 1,-3,-5 !

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Example Question:

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The example I provided is in standard form.

Here's what I did:

Step 1: Move the "C" to the other side (in this case it's negative 14, so you add 14 to both sides of the equation to move it).

Step 2: Leave a blank after Ax²+Bx. In this case, it'll look like: X²+6x+_____= 14.

Step 3: Use the box to find the missing "C". Idk if you can see the photo after the 1st one, but I circled the spaces in green. Those spaces indicate 2 factors that add up for B (in this case, 6). Those same factors will eventually multiply each other to get 9.

Step 4: Give the new "C" to both sides of the equation. What this means is that after you multiply the factors on the outside of the box, you put the number on both sides. The 3rd picture I drew is the process of finding the outer factors (by plugging in 3x to the spaces that were circled).

If you can't see it, it's (X+3)•(X+3).

The 4th picture is me plugging the new "C" (9) to both sides of the equation. 3 times 3 is 9. You multiply the 3's on the outside to get the factors on the inside.

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What this means is that you take the factors on the outside and rewrite it in perfect square form. like shown in picture 5. If you can't see it, it's like this:

(X+3)•(X+3) turns to (X+3)²=23.

The 23 was from adding 14+9 together.

So the final Answer would be:

(X+3)²=23.

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3 years ago
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